Problem: Simplify the following expression: $x = \dfrac{p^2 - 19p + 90}{p - 10} $
Explanation: First factor the polynomial in the numerator. $ p^2 - 19p + 90 = (p - 10)(p - 9) $ So we can rewrite the expression as: $x = \dfrac{(p - 10)(p - 9)}{p - 10} $ We can divide the numerator and denominator by $(p - 10)$ on condition that $p \neq 10$ Therefore $x = p - 9; p \neq 10$